Comparative analysis of ventricular stiffness across species

Abstract Investigating ventricular diastolic properties is crucial for understanding the physiological cardiac functions in organisms and unraveling the pathological mechanisms of cardiovascular disorders. Ventricular stiffness, a fundamental parameter that defines ventricular diastolic functions in chordates, is typically analyzed using the end‐diastolic pressure–volume relationship (EDPVR). However, comparing ventricular stiffness accurately across chambers of varying maximum volume capacities has been a long‐standing challenge. As one of the solutions to this problem, we propose calculating a relative ventricular stiffness index by applying an exponential approximation formula to the EDPVR plot data of the relationship between ventricular pressure and values of normalized ventricular volume by the ventricular weight. This article reviews the potential, utility, and limitations of using normalized EDPVR analysis in recent studies. Herein, we measured and ranked ventricular stiffness in differently sized and shaped chambers using ex vivo ventricular pressure‐volume analysis data from four animals: Wistar rats, red‐eared slider turtles, masu salmon, and cherry salmon. Furthermore, we have discussed the mechanical effects of intracellular and extracellular viscoelastic components, Titin (Connectin) filaments, collagens, physiological sarcomere length, and other factors that govern ventricular stiffness. Our review provides insights into the comparison of ventricular stiffness in different‐sized ventricles between heterologous and homologous species, including non‐model organisms.


| INTRODUCTION
Accurately evaluating ventricular diastolic properties is crucial for interpreting cardiac functions as a blood pump and understanding the pathological mechanisms of cardiovascular disorders.Investigating ventricular diastolic properties using pressure-volume analysis in the ventricle has been a cornerstone of cardiac dynamics studies (Frank, 1895;Patterson & Starling, 1914).Notably, several studies have aimed to provide comprehensive insights into cardiac functions (Burkhoff et al., 2005;Mirsky, 1984;Suga, 1969).Currently, ventricular diastolic functions have been examined in various species, ranging from mammals to fish, utilizing cardiac stiffness analyses, cardiac hemodynamics imaging, and molecular biological experiments, demonstrating that ventricular diastolic functions differ among chordates (Burkhoff et al., 2005;Farrell, 1991;Kraner & Ogden, 1956;Warburton & Fritsche, 2000;Wu et al., 2004).For instance, in healthy adult humans, early diastolic ventricular filling driven by releasing the elastic energy stored during deformation in the ventricular systole dominates atrioventricular inflows, whereas ventricular filling in many fishes primarily depends on atrial contraction.
A counterclockwise loop emerged with each cardiac cycle when sequential pressure and volume dynamics of the mammalian left ventricle were recorded and plotted on a graph, with ventricular pressure on the vertical axis and ventricular lumen volume on the horizontal axis (Burkhoff et al., 2003).Based on hemodynamic principles, the physiological significance of the ventricular pressurevolume relationship was confirmed by deterministic relationships in myocardial energetic studies, such as oxygen consumption and time-varying elastic models (Suga, 1979;Suga, 1990).Moreover, analysis of ventricular pressurevolume dynamic patterns has been demonstrated to be effective in inferring ventricular systolic and diastolic functions, aiding in understanding cardiac physiology and pathology (Burkhoff et al., 2003).
At the outset, it is important to appreciate that there are two distinct, although intimately interrelated, aspects to assessing cardiac stiffness (Burkhoff et al., 2005;Villalobos Lizardi et al., 2022).One aspect involves the assessment of ventricular stiffness, which pertains to the systolic and diastolic properties of the ventricle as a hemodynamic pump.The other aspect focuses on myocardial stiffness, which assesses the intrinsic properties of the myocardium and cardiomyocyte.Ventricular stiffness, or its reciprocal, ventricular compliance, is an important parameter for defining ventricular filling and has been examined using the ventricular pressure-volume analysis (Burkhoff et al., 2005).The change in ventricular end-diastolic pressure relative to the change in ventricular volume (dP/dV) during the ventricular filling phase, from mitral valve opening to closing, represents ventricular stiffness and demonstrates a nonlinear curve (Figure 1a) (Diamond et al., 1971;Grossman et al., 1973).These end-diastolic pressure-volume relationship (EDPVR) curves deform their slopes to reflect ventricular material properties (sarcomere extensibility and extracellular matrix [ECM] accumulation), physiological remodeling with normal growth, pathological remodeling (fibrosis, ischemia, edema, cardiac hypertrophy, heart failure, and myocardial infarction), and structural changes (malformation of the trabeculae carnies and valves) (Mirsky & Pasipoularides, 1990;Wisneski & Bristow, 1978).Therefore, ventricular stiffness reflects myocardial properties, ventricular structure, and ventricular geometry.Evaluating EDPVR curves is clinically significant, and the curve's position changes depending on the types of ventricular impairment.For instance, the curve shifts to the left in heart failure with preserved ejection fraction (HFpEF) and to the right in heart failure with reduced ejection fraction (HFrEF), compared with that in a healthy heart (Borlaug, 2014;Schwarzl et al., 2016).However, EDPVR analysis using conductance catheters has limited clinical applicability because of its high invasiveness.Recently, minimally invasive measurement methods have been proposed to predict the ventricular stiffness index from a single heartbeat and echography imaging (Kasner et al., 2015;Klotz et al., 2006).
Consequently, assuming that two differently sized hearts have geometric similarities associated with development of the thickness of the ventricular walls and exhibit equal myocardial stiffness, the larger ventricle should exhibit lower ventricular pressure than the smaller one when both are filled with the same blood volume.In this case, ventricular stiffness depends on ventricular lumen volume, and the two hearts exhibit different dP/dV.Therefore, comparing ventricular stiffness in chambers with varying volume capacities poses a challenge (Burkhoff et al., 2003;Burkhoff et al., 2005).To solve this problem, approaches are needed to calculate the ventricular stiffness index from the normalized EDPVR curve, considering each sample's ventricular lumen volume and mass.Recently, we compared ventricular stiffness among other species using the normalized EDPVR assessment system and evaluated the relative diastolic ventricular stiffness of four types of hearts from three species: Wistar rats (Rattus norvegicus), red-eared slider turtles (Trachemys scripta elegans), masu salmon (landlocked type, Oncorhynchus masou masou), and cherry salmon (sea-run type) (Honda et al., 2018;Usui et al., 2022).These animals were selected because they met the experimental requirements of availability, ease of husbandry, and ventricular size, allowing the stable placement of conductance catheters.
In this review, we consolidate our findings with literature evaluating ventricular stiffness in chambers of different sizes across species.In addition, we discuss the mechanical effects of intracellular and extracellular viscoelastic components that govern ventricular stiffness.

VENTRICULAR STIFFNESS
This section highlights the potential challenges in comparing the ventricular stiffness in ventricles of different sizes and proposes solutions.Initially, we assumed three types of ventricles with different stiffness levels (standard, stiff, and compliant), all of the same size.Next, we plotted their end-diastolic pressure-volume data (Figure 1a).Herein, the middle curve was assumed to be pressure-volume plots of a healthy ventricle as a standard EDPVR.The stiffer ventricle exhibited a leftward shift and a steeper EDPVR curve than the standard (Maurer et al., 2006).Conversely, the ventricle with increased compliance displayed a gentle slope and a rightward shift in the EDPVR curve (Maurer et al., 2006).
Each EDPVR curve was described as an exponential fit based on the following equation: where P indicates the ventricular pressure and α, β, and γ are constants describing the ventricular exponential pressure-volume property (Burkhoff et al., 2005;Mirsky, 1976).The constant β is the ventricular stiffness index representing the curve's slope.γ is the intercept on the pressure axis (α = −γ), and the curve-fitting formula was forced through the origin.V represents the ventricular volume, synonymous with the volume of injected saline in a ventricle to measure ventricular pressure.In EDPVR analysis, saline was infused at a constant flow rate using an auto-infusion pump into the ventricles, ligated in the proximal ventricular side of the aorta or bulbous arteriosus to prevent leakage.In addition to Equation 1, several curve-fitting formulas have been proposed to calculate the ventricular stiffness index (Burkhoff et al., 2005).In Equation 1, β is expressed in milliliters −1 and depends on the ventricular size (Mirsky, 1976).Therefore, as a next step, if the three ventricles had different sizes, the position relationships of the EDPVR curves may not correlate with the assumed ventricular stiffness.A previous study proposed a strategy that compared the dimensionless ventricular stiffness index β, multiplied by end-diastolic volume normalized in the volume dimension from 0 to 30 mmHg (Klotz et al., 2006).Volume-normalized EDPVR curves showed a similar shape independent of the heart-healthy conditions, and the uniqueness of this curve contributed to estimating EDPVR (Klotz et al., 2006).
(1) P = e V + , Normalizing EDPVR using optimized parameters has been suggested to allow for finding the curve's uniqueness.Clinical investigations have sometimes normalized ventricular volume by body surface area (Gaasch et al., 1976).The relation between ventricular stiffness and ventricular volume/myocardial volume ratio has been found to distinguish between ventricular hypertrophy and increasing ventricular stiffness (Gaasch et al., 1976).The stress (force per unit myocardial area)-strain (segment length relative to reference length) relationship analysis is a typical evaluation method for assessing intrinsic myocardial stiffness, locally applied to a small volume of the myocardium, independent of ventricular size (Takaoka et al., 2002).It is based on Laplace's law and assumes an ellipsoidal spherical ventricle (Mirsky et al., 1987).Rat ventricles are mirrored as ellipses.The red-eared slider turtle ventricles also exhibit an ellipsoidal shape when the gubernaculum cordis is detached (Honda et al., 2018).However, their ventricles exhibit a cone shape when connected to the gubernaculum cordis.Masu and cherry salmons have pyramidal-shaped ventricles (Usui et al., 2022).Therefore, the stress-strain relationship analysis is not necessarily appropriate for measuring myocardial stiffness across animal species or would require complicated calculations to compensate for their ventricular morphology to compare the hearts of different structures.The ventricular systolic index, E max , was strongly influenced by ventricular size.This problem was solved by converting the systolic pressure-volume relationship into an end-systolic force-length relationship per unit myocardial mass of the ventricular wall (Suga et al., 1984).The ventricular lumens of red-eared slider turtles and masu and cherry salmons are arranged in trabeculated myocardial cells.Considering their spongy layer, correction for diastolic ventricular stiffness is difficult in this calculation method.Therefore, appropriately corrected ventricular stiffness indices must be explored to compare ventricular diastolic functions across a wide range of animal species and ventricles of different sizes by modifying the curvefitting formulas of EDPVRs.
To overcome this challenge, we calculated the ventricle stiffness using EDPVR curves based on the relationship between ventricular lumen volume per gram of ventricle and ventricular pressure.We substituted the following formula into parameter V in Equation 1: where V is the total volume of saline infused into the ventricle at time t, v 0 = 0, and it is described in milliliters; m represents the ventricular weight.In this case, β' has the units of gram × milliliters −1 , and the ventricle size is considered.
Our research group previously conducted ex vivo EDPVR analysis on the hearts of Wistar rats, red-eared slider turtles, and masu and cherry salmons using the same experimental system (Table 1) (Honda et al., 2018; (2 Note: Values are presented as the mean ± standard deviations.

Animal
Protocol of ex vivo end-diastolic pressure-volume relationship (EDPVR) analysis: Experimental animals were euthanized, and their hearts were removed.A catheter was inserted into the fresh ventricle through the atrioventricular valve and fixed by ligation.The ventricular lumen was washed out using phosphatebuffered saline with 10 U/mL heparin and 10 mM 2,3-butanedione monoxime.The aortic valve was then ligated.To measure the ventricular pressure, saline solution was injected into the ventricles using an infusion pump (TE-311, Terumo Corp.).The ventricular pressure data were recorded at 400 Hz using an analysis software (LabChart 7, ADInstruments Pty Ltd.) by mediating a transducer (DT-XX, Argon Medical Devices, Inc.), an amplifier (AP-641G, NIHON KOHDEN Corp.), and an AD converter (Power Lab 8/30, ADInstruments Pty Ltd.).Calibration of the pressure in the measurement equipment was performed for each trial.The sensor was connected to the sphygmomanometer before and after pressure measurement.The sphygmomanometer (Sanden Medical Industry Corp.) was operated in the following order: 0, 50, 0 mmHg.Next, the ventricular lumen fluid was drained, and ventricular weights were measured using an electronic balance.The ventricular stiffness index β was calculated from the EDPVR plots in Figure 1b.In these plots, the x-axis represented the ventricular volume, equivalent to the volume of saline solution injected by the infusion pump, while the y-axis represented the diastolic ventricular pressure.The ventricular stiffness index β', normalized by ventricular weight, was calculated from plots in Figure 1c where the x-axis represented the ventricular volume per gram of ventricle-computed by dividing the ventricular volume by ventricular weight-and the y-axis represented the ventricular pressure.The curve-fitting equation of EDPVR plots described the exponential growth with a constant doubling time.For detailed information on curve fitting, refer to the RELATIVE ANALYSIS OF VENTRICULAR STIFFNESS in the main text.Usui et al., 2022).Saline was injected at a constant rate into their (left) ventricles.Their pressure-volume relationships were plotted on the same graph until the intraventricular pressure reached ~ 20 mmHg (Figure 1b).Subsequently, EDPVR curves were replotted for the ventricles of Wistar rats, red-eared slider turtles, and masu and cherry salmons, with ventricular volume divided by ventricular weight as the horizontal axis (Figure 1c).The relative ventricular stiffness indices from the replotted normalized EDPVR curves were calculated using Equation 1(Table 1).Consequently, the relative ventricular stiffness indices were rearranged in the order of Wistar rats > cherry salmon > red-eared slider turtles > masu salmon.
The Wistar rat's ventricle was estimated to be the stiffest of the four types.These relative ventricular stiffness indices have also been calculated for three frog species, namely aquatic African clawed frogs (Xenopus laevis), terrestrial or semiaquatic black-spotted pond frogs (Pelophylax nigromaculatus), and Japanese common toads (Bufo japonicus formosus), by the same normalization method (Ito et al., 2023).The ventricles of black-spotted pond frogs and Japanese common toads are shown to be stiffer than those of African clawed frogs, implying that their ventricles undergo stiffening in the process of adapting to terrestrial life (Ito et al., 2021).The normalized EDPVR curves may help evaluate the relative ventricular stiffness among various animals and provide a comprehensive understanding of their ventricular diastolic properties.

| ELASTIC COMPONENTS OF THE VENTRICULAR MYOCARDIUM
This section discusses factors contributing to inter-and intra-species differences in ventricular stiffness, supported by relevant data.We believe that the difference in ventricular stiffness among Wistar rats, red-eared slider turtles, and two salmon fishes could be explained by factors, such as the number of amino acids in the spring functional region of Titin (Connectin, encoded by ttn) expressed in the ventricles, collagen fiber deposits in the ventricles, and the range differences in physiological sarcomere length in the cardiomyocyte.

| Elastic region length of titins
Sarcomeres in cardiomyocytes mainly comprise three filaments, namely actin, myosin, and Titin (Figure 2a).Titins are high-molecular-weight proteins (3-4 MDa) that extend across half the sarcomere length from the Z-disc to the M-line (Maruyama et al., 1976;Wang et al., 1979).Titin is responsible for generating passive tension in cardiomyocytes (Granzier & Irving, 1995;Linke et al., 1994).In a sarcomere's I-band, Titins have an unstructured region that reserves elastic potential energy, the N2A element, the N2B element, the middle tandem immunoglobulinlike (Ig) segment, and the PEVK (proline-glutamatevaline-lysine resides repeats and E-rich motifs) segment (Bang et al., 2001;Freiburg et al., 2000).Conformational changes in these elastic elements are believed to support sarcomere function as biological springs.Human cardiomyocytes express several Titin isoforms, including N2B, N2BA, Novex1, and Novex2, and two short isoforms, Novex3 (0.63 MDa) and Cronos (2.2 MDa) (Bang et al., 2001;Freiburg et al., 2000).The N2BA isoform contains the N2B and N2A elements.The N2B isoform lacks the N2A element and the middle tandem Ig segment, except for I27, by splicing.It has fewer amino acids in its PEVK segment than the N2BA isoform.Novex1 has the N2B element, I16, I27, and PEVK segment in the unstructured region; Novex2 has the I17, I27, and PEVK segment in the unstructured region; and Novex3 has a unique C-terminal sequence, localizes in the nucleus during the embryonic stage of mice, and regulates nuclear stiffness in cardiomyocytes (Hashimoto et al., 2018).Cronos lacks the N-terminal region of Titin and supports partial sarcomere formation.The expression patterns of Titin isoforms in the heart have been extensively studied in mammals (mice, rats, rabbits, dogs, humans, pigs, cows, and sheep) (Cazorla et al., 2000;Locker & Wild, 1986), birds (chickens and thrushes) (Locker & Wild, 1986), and fish (masu salmon, cherry salmon, zebrafish (Danio rerio), and rainbow trout (Oncorhynchus mykiss)) (Hanashima et al., 2017;Patrick et al., 2010;Usui et al., 2022).Titin isoforms, including N2B elements, are found in cardiomyocytes but not skeletal muscle.The ratio of N2B to N2BA isoforms is linked to the ventricular diastolic function.
The myocardium of neonates shows a higher expression ratio of the N2BA isoforms and is more compliant than that of the adult heart (Lahmers et al., 2004).Hearts of patients with diastolic left ventricular dysfunction, characterized by increasing passive tension, as well as athletes' hearts show a higher expression ratio of the N2BA isoform relative to healthy hearts (Hidalgo & Granzier, 2013;Kellermayer et al., 2021;Trombitas et al., 2001).Sprague Dawley rats with rbm20 knockout display diastolic dysfunction due to impaired splicing out of the N2A element and increased expression of the N2BA isoform (Guo et al., 2012).Mutations in TTN and RBM20 account for approximately 25% and 3% of cases of dilated cardiomyopathy in humans, respectively (Guo et al., 2012;Herman et al., 2012).Consequently, regulating cardiac stiffness through the expression patterns of Titins with longer or shorter unstructured regions has emerged as a novel therapeutic approach for cardiomyopathy.Mammals have only one ttn gene in their genome.In contrast, two ttn genes, ttn.1 and ttn.2, have been identified in teleosts, such as brown trout (Salmo trutta, GeneID: 115155650 and 115155651) and zebrafish (GeneID: 100001684 and 317731; Figure 2b).Notably, multiple isoforms of ttn.1 and ttn.2 are expressed in the zebrafish heart (Hanashima et al., 2017).The diversity of ttn genes and Titin isoforms might also be implicated in the regulation of myocardial passive stiffness.Furthermore, post-translated modifications (oxidation, phosphorylation, and deacetylation) in the N2B element, middle tandem Ig segment, and PEVK segment regulate the stiffness of the ventricular myocardium (Koser et al., 2019).
A major Titin expressed in the left ventricles of Wistar rats has a lower molecular weight than that expressed in the red-eared slider turtle ventricles (Wistar rats: 3.0 MDa, red-eared slider turtles: 3.5 MDa) (Honda et al., 2018).The left ventricles of Wistar rats predominantly expressed the N2B isoform (Figure 2b).However, the red-eared slider turtle ventricles expressed the N2BA isoform, containing both N2B and tandem N2A elements.The N2B element includes 876 and 1302 amino acids in Wistar rats and red-eared slider turtles, respectively.The PEVK segment comprises 204 and 821 amino acids in Wistar rats and red-eared slider turtles, respectively.Based on the comparison of these, it has been predicted that the ventricular myocardium in red-eared slider turtles is more compliant than that in Wistar rats (Honda et al., 2018).This prediction is consistent with normalized EDPVR analysis results, which demonstrate that Wistar rat's ventricles are stiffer than red-eared slider turtle ventricles (Figure 1c and Table 1).Therefore, the length of the unstructured region and the number of amino acids constituting Titin's N2B element and PEVK segment determine the magnitude of passive tension generation in cardiomyocytes.By extension, obtaining the amino acid sequence of Titin expressed in the hearts of experimental animals under study from the genomes or gene expression platforms may provide a rough prediction of their ventricular diastolic properties.The hearts of red-eared slider turtles and fishes express longer unstructured regions of Titins than those of mammals, which may be used as a model for dilated cardiomyopathy without gene manipulations.
The viscoelastic properties of cardiomyocytes are not solely dependent on Titin.Recently, it was reported that stabilizing the non-sarcomeric cytoskeleton contributes to cardiac stiffness.Emerging evidence suggests that posttranslational modifications (acetylation and detyrosination) and polymerization of microtubules alter cardiomyocyte viscoelastic stiffness, and these changes are associated with pathological cardiac remodeling through tubulin stabilization (Caporizzo et al., 2019).Tubulin stabilization and metabolization are therapeutic targets for reducing stiffness in heart failure (Caporizzo & Prosser, 2022).The contribution of passive tension generated by microtubules and intermediate filaments to ventricular stiffness has been investigated alongside Titin and collagen.However, a report suggests that their contribution is smaller than that of Titin and collagen in healthy Sprague Dawley rat myocardium, particularly within the range of the mammalian physiological sarcomere length (Granzier & Irving, 1995).

| Collagen fiber deposition in the ventricular myocardium
The ECMs in the animal heart support the tissue structure, being localized between myocardial cells and around blood vessels (Eghbali & Weber, 1990).The cardiac ECMs form a complex network within the inter-myocardial cell space, consisting of various structural and non-structural proteins, including glycoproteins (several collagens, fibronectin, laminin, thrombospondins, secreted protein acidic and rich in cysteine, tenascin, osteopontin, periostin, and CCNs), elastin, glycosaminoglycans (hyaluronan and heparan sulfate), and proteoglycans (versican, neurocan, brevican, aggrecan, perlecan, type XVIII collagen, agrin, syndecans, and biglycan) (Rienks et al., 2014).In response to aging, pressure overload, dilated myopathy, HFpEF, and heart inflammation, cardiac ECMs are secreted or degraded in the heart to maintain homeostasis of the cardiovascular system (Bashey et al., 1992;Nikolov & Popovski, 2022).The hearts of neonatal mammals, urodeles, and teleosts contain abundant cardiac ECMs, such as fibronectin and periostin, with a low percentage of collagens.In contrast, the hearts of adult mammals exhibit reduced levels of fibronectin, becoming stiff with a high percentage of collagens (Hortells et al., 2019).
Collagens are the main fibrous component of the cardiac ECMs (Bashey et al., 1992;Nikolov & Popovski, 2022).In patients with heart failure, collagen accumulation is associated with the severity of ventricular diastolic dysfunction (Mirsky & Pasipoularides, 1980;Peterson et al., 1978).In particular, myocardial fibrosis, characterized by the excess deposition of ECMs, including abnormal collagen architectures, is observed in varying degrees in patients with HFpEF and is associated with a worse prognosis, as supported by a study using late gadolinium-enhanced magnetic resonance imaging and autopsy (Shah et al., 2020).In addition, a large experimental animal model study shows that the progression of HFpEF from pressure overload is accompanied by pathologic shifts in the collagen matrix microstructure, in addition to fibrosis induced by the collagen content (Torres et al., 2020).These results underscore the relevance of collagen in myocardial fibrosis.The collagen superfamily includes 28 genes in humans, and several valuations exist by modification of αchains and isoforms (Ricard-Blum, 2011).While there are species-specific differences in collagen types among mammals, previous reports have identified 24 types of collagens expressed in the heart, including those implicated in heart disease (Frangogiannis, 2019).The epimysium and perimysium in adult mammals primarily contain type I collagen (Heeneman et al., 2003).Type I collagen constitutes approximately 85% of cardiac ECMs.Type III collagen is expressed in the endomysium, while types V and XI collagens participate in valve formation.Types XIII, XVII, XXI, XXII, and XXV collagens are minimally expressed in the myocardium.Type XXVII collagen is involved in coronary vessel formation, type VI collagen is expressed in myocardial vessels, and type IV collagen is found in the basement membrane (Esmaeili et al., 2020;Frangogiannis, 2019;Heeneman et al., 2003;Nikolov & Popovski, 2022).Zebrafish possess 58 collagen genes, and the expression of 36 collagen genes has been identified in their hearts (Nauroy et al., 2018;Sarohi et al., 2022).Zebrafish predominantly express type I collagens (co-l1a1a, col1a1b, and col1a2), followed by types V, VI, and IV collagens (Sarohi et al., 2022).The cardiac ECMs of adult mammals and urodeles involve type III collagen; however, there is no expression of type III collagen in the cardiac ECMs of teleosts (Hortells et al., 2019).
In the ventricular myocardium, collagen is cross-linked through the catalysis of lysyl oxidases, transglutaminases, and non-enzymatic advanced glycation end products and accumulates.All three catalytic reactions are thought to be important in the progression of cardiac fibrosis (Neff & Bradshaw, 2021).Cross-linked collagens show collagenase resistance compared to the non-cross-linked type (Vater et al., 1979).In the lysyl oxidase pathway, collagen cross-linking is initiated by the oxidation of lysine and hydroxylysine residues of collagen; the resulting allysine (αaminoadipic acid-δsemialdehyde) and hydroxy-allysine (hydroxy-αaminoadipic acid-δsemialdehyde) then form immature cross-linking.Ultimately, further modified collagens are condensed into mature di-to tetra-valent crosslinked, degradation-resistant structures (Eyre et al., 1984;Piersma & Bank, 2019).Transglutaminases catalyze the formation of ε (γ-glutamyl)-lysine cross-link between lysine and glutamine residues in transmembrane proteins (integrins, syndecans, platelet-derived growth factor receptor, and low-density lipoprotein receptor-related protein) and other transmembrane proteins or ECMs (Aeschlimann & Thomazy, 2000).The specific lysine and glutamine residues in collagens modified by transglutaminase are unclear (Neff & Bradshaw, 2021).Advanced glycation end products glycate lysine residues in fibrous collagen, competing with lysyl oxidase for some lysine residues (Saito & Marumo, 2013).In addition, mice lacking the genes for fibromodulin (fmod), periostin (postn), thrombospondin1 (thbs1), or secreted protein acidic and rich in cysteine (sparc) show abnormal collagen content, suggesting that these molecules are involved in the regulation of collagen cross-linking (Andenaes et al., 2018;Schellings et al., 2009;Shimazaki et al., 2008;Xia et al., 2011).In mice lacking genes involved in ECM cross-linking or inhibiting these catalytic activities, myocardial stiffness is reduced (Neff & Bradshaw, 2021).Matrix metalloproteinases (MMPs) and cysteine protease cathepsins are responsible for degrading the ECM and regulating total collagen content.The enzymatic activities of MMPs are inhibited by tissue inhibitors of MMPs (TIMPs) (Nagase et al., 2006).The human myocardium expresses MMP1, MMP2, MMP3, MMP9, MMP13, and MMP14, which degrade collagen and other substrates (Spinale, 2002).Fibrotic collagen is the dominant cross-linking of hydroxy-allysine type by lysyl hydroxylase 2 (Piersma & Bank, 2019;van der Slot et al., 2005).Cathepsin K, exhibiting a cardioprotective effect, more efficiently degrades strongly cross-linked collagen by hydroxy-allysine compared with MMPs (Guo et al., 2018;Kafienah et al., 1998).In addition, the differences in ECM-based cardiac stiffness are indicated to be related to the potential of heart regeneration (Hortells et al., 2019).Mammalian hearts form permanent scars after myocardial infarction.In contrast, the post-injury scar in the heart in zebrafish disappears, and the heart regenerates (Poss et al., 2002).As the progression of the degradation-resistant collagen is suppressed in zebrafish hearts 1 month after heart cryoinjury, the collagen crosslinking process after myocardial infarction may differ between mammals and zebrafish (Akam et al., 2023).
Recently, we reported that the ventricles of the compact layer in cherry salmon at 29-30 months post-fertilization contain more collagen fibers than those in masu salmon (p = 0.0003) (Usui et al., 2022).The non-normalized EDPVR curve for masu salmon is drawn on the left compared with that for cherry salmon (Figure 1b).In simpler terms, the end-diastolic pressure of masu salmon is higher than that of cherry salmon at the same ventricular volume.However, it is important to note that the ventricle of cherry salmon is larger and approximately 18 times heavier than that of masu salmon (Table 1).By considering the end-diastolic pressure of both fish species and incorporating normalized ventricular volumes using their ventricular weights following Equations 1 and 2, their EDPVR curve positions and relative ventricular stiffness indices were reversed (Figure 1c and Table 1).Given the similarity in the expression patterns of Titin in the hearts of both fish, these findings imply that the ventricle of cherry salmon becomes stiffer than that of masu salmon, possibly due to an increase in the collagen content of the compact layer (Usui et al., 2022).
Rainbow trout and red-eared slider turtles exhibit heightened collagen accumulation in their ventricles, resulting in increasing ventricular stiffness when exposed to water temperatures in the range of 4-5°C (Keen et al., 2015;Keen et al., 2016).In that case, their EDPVR curve shifts to the left and becomes steeper than that of the control group (Figure 1a).Moreover, the rainbow trout displays an increase in myocardial mass of the spongy layer under such conditions (Keen et al., 2015;Klaiman et al., 2011).Although most animals suppress cardiac contractile functions at low temperatures by reducing Ca 2+ sensitivity, fish that have adapted to such environments maintain their cardiac functions (Churcott et al., 1994;Harrison & Bers, 1990;Klaiman et al., 2014;Liu et al., 1990;Liu et al., 1993;Shiels et al., 2000;Stephenson & Williams, 1985).Cold conditions are thought to induce cardiac remodeling driven by hemodynamic load, characterized by high blood viscosity, consequently increasing ventricular stroke volume in certain fish species (Clark & Rodnick, 1999;Graham & Farrell, 1989;Keen et al., 2015;Keen et al., 2016;Klaiman et al., 2011).The increased cardiac stiffness observed during cold acclimation is likely a compensatory mechanism to prevent excessive stretching of the myocardium under mechanical stress.The extension of the myocardium upregulates the gene expression of col1a3 and timp2 through TGF-β signal and the MAPK pathway, leading to collagen accumulation in the heart (Johnston & Gillis, 2018;Johnston & Gillis, 2020;Keen et al., 2015).Furthermore, the expression levels of mmp2, mmp9, and mmp13 decrease (Keen et al., 2015).These thermal cardiac phenotypes observed in most fish are seasonal and reversible (Klaiman et al., 2011;Shiels et al., 2011).The downregulation of type I collagens is mediated by miR-29b (Johnston et al., 2019).Cold acclimation also induces an increase in lipid biosynthesis and βoxidation in rainbow trout (Driedzic et al., 1996;Driedzic & Gesser, 1994); however, the direct impact of ventricular stiffness on the cold-associated metabolic changes remains largely unknown.Some recent reviews provide a more comprehensive understanding of temperaturedependent cardiac remodeling (Johnston & Gillis, 2022;Keen et al., 2017).

| The range of physiological sarcomere lengths
The range of physiological sarcomere lengths of normal mammalian cardiomyocytes between Z-lines is 1.8-2.2μm (Allen & Kentish, 1985).However, peak active tension occurs in the cardiomyocytes of rainbow trout at a sarcomere length of 2.6 μm (Shiels et al., 2006).Cardiomyocytes of Wistar rats and rainbow trout generate active tension with sarcomere length dependence, increasing Ca 2+ sensitivity in the normal and above the physiological sarcomere length range.Rainbow trout cardiomyocytes have shown higher Ca 2+ sensitivity than Wistar rat cardiomyocytes, generating greater active tension at physiological Ca 2+ concentrations (Patrick et al., 2010).This responsiveness of sarcomere length suggests that ventricular myocardium properties of fish are more compliant than those of mammals.In addition, force-sarcomere strain analysis showed that the isolated cardiomyocyte stiffness of Wistar rats was 2.8 times higher than that of red-eared slider turtles (Honda et al., 2018).
The passive tension of mammalian cardiomyocytes within the physiological sarcomere lengths mainly depends on Titin.As the myocardial tissue elongates, collagen also contributes to resisting myocardium stretching; however, the collagen-based passive tension is relatively small compared with that induced by Titin (Granzier & Irving, 1995).The Titin-dependent passive tension is more pronounced in myocardial tissue that expresses a higher proportion of N2BA isoforms than in other myocardial tissues expressing N2B isoforms (Wu et al., 2000).The N2BA-like isoform expressed in cardiomyocytes of the ventricles of rainbow trout accounts for approximately 38% of the total Titin expression; however, Titin-based passive tension at sarcomere lengths beyond the mammalian working range was generated (Patrick et al., 2010).Titins in the ventricles of rainbow trout were modified with less phosphorylation, which may be responsible for the lower myocardial stiffness (Patrick et al., 2010).

| LIMITATIONS AND CONCLUSION
In addition to ventricular stiffness, myocardial stiffness is another essential indicator in the overall assessment of cardiac stiffness (Burkhoff et al., 2005;Villalobos Lizardi et al., 2022).One major limitation of the study described in this review is that EDPVR analysis only assesses global chamber stiffness.The pressure-volume analysis does not evaluate the local tissue stiffness derived from the stressstrain relationship based on Young's and shear modulus.The stress-strain relationship analysis for intrinsic myocardial properties is developed in several tests for the anisotropic elastic myocardium, providing stiffness values for local axial, transverse, and shear properties in the microscopic structure of the myocardium, independent of ventricular size (Villalobos Lizardi et al., 2022).To ensure a comprehensive evaluation of cardiac stiffness, it is crucial to incorporate both stiffness analyses.
This review describes the calculation method of the relative ventricular stiffness indices using normalized EDPVR by plotting ventricular pressure against ventricular volume per ventricle weight.Index differences in Wistar rats and red-eared slider turtles correlate with the number of amino acids constituting the spring functional region of Titin (Honda et al., 2018).In the cases of masu and cherry salmons, these indices are reflected by the ratio of collagen accumulation in the ventricular myocardium wall (Usui et al., 2022).Additionally, these indices also seem to correlate with the relationship between sarcomere length and passive tension production in both mammals and teleosts (Shiels et al., 2006).Notably, while comparing the relative ventricular stiffness indices using ventricular volume per ventricular weight provides a reasonable interpretation to some extent, there is currently insufficient theoretical evidence for the normalizing method.Therefore, it is imperative to approach the relative ventricular stiffness index derived from EDPVR data, utilizing ventricular volume per ventricular weight on the horizontal axis, with caution and suspicion at this time.To date, changes in ventricular weight, ventricular wall thickness, fibrosis, hemodynamics, and collagen gene expression have been analyzed in detail in mouse models of HFpEF induced by obesity through high-fat and high-sucrose diets as well as in some diabetic model animals (Croteau et al., 2020;Gueorguiev et al., 2001;Woodiwiss et al., 1996).Accordingly, to establish the ex vivo EDPVR analysis proposed as a method based on a scientific rationale, it should be examined to verify whether the relative ventricular stiffness indices accurately rank ventricular diastolic properties in these model animals.
Few studies have tried to compare cardiac stiffness among different species with hearts of varying sizes.Therefore, there is a need for investigation into ventricular stiffness in various chordates.In this context, physiological blood pressure difference is one of the parameters that should be considered.Generally, aquatic organisms, excluding cetaceans, have a lower aortic blood pressure than mammals (20-60 vs. 60-120 mmHg) (Nishiyama et al., 2022).The ex vivo EDPVR analysis in this review calculated and compared ventricular stiffness indices within the range of 0-20 mmHg of ventricular lumen pressure.This range includes pressures exceeding physiological end-diastolic levels.For example, the (left) ventricle end-diastolic pressure in humans is 5-12 mmHg, which is higher than the corresponding value in fish.
Lipids hold the potential to serve as determinants of cardiac stiffness.Lipid compositions in the heart have been studied in several animals, including mice, rats, dogs, ox, redfish, and Atlantic salmon, revealing differences among species (Connellan & Masters, 1965;Joensen & Grahl-Nielsen, 2000;Martinez-Rubio et al., 2012;Nazir et al., 1970;Tham et al., 2018;Wheeldon et al., 1965).It should be noted that these previous studies are not strictly comparable owing to the different extraction and analysis methods.Additionally, within the same species, cardiac lipid compositions vary with age, diet, exercise, and the increasing cardiac pressure overload induced by transverse aortic constriction (TAC) (Martinez-Rubio et al., 2012;Tham et al., 2018).Increased ventricular stiffness has been observed in the hearts of animals treated for TAC (Richards et al., 2019;Torres et al., 2020).Furthermore, slight increases in sphingolipid contents of the heart have been demonstrated in mice after TAC surgery (Richards et al., 2019).However, further verifications are necessary to determine the contribution of increased sphingolipids and species differences in lipid compositions to ventricular stiffness.
This review proposes a provisional evaluation method for comparing ventricular stiffness, an indicator of ventricular diastolic properties, among chordates with varying ventricular sizes and shapes.This ex vivo EDPVR analysis provides the relative ventricular stiffness, disregarding blood loading and employing 0 mmHg as a baseline, to delineate the relationship between ventricular volume per 1 g of myocardium and ventricular pressure.However, the validation of this normalization method for ventricular stiffness is insufficient.Therefore, in the future, rigorous scientific evidence should be established by combining our proposed analysis with the multidimensional and multiscale cardiac stiffness evaluation methods (Villalobos Lizardi et al., 2022) pioneered by the great predecessors.This will contribute to a comprehensive assessment of ventricles across various species and confirm consistency.Interpreting physiological ventricular diastolic functions based on ventricular pressure-volume relationships in various animal ventricles, undergoing changes in their weights and lumen volumes as an adaptive process to physical growth and chronic mechanical loading of the heart, may yield clinically valuable approaches.Such approaches may include defining early determinants of ventricular dysfunction, predicting its risk, and preventing its progression.In addition, we believe that comparing cardiac diastolic properties in numerous species and the same species reared in different environments will provide new insights into the adaptive evolution of cardiac physiological function, contributing to advances in cardiac physiology.

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I G U R E 1 End-diastolic pressurevolume relationship (EDPVR) curves.(a) An image of EDPVR curves in the different scores of ventricular stiffness.The horizontal axis represents ventricular volume, and the vertical axis indicates ventricular pressure.The left, middle, and right curves indicate that the chamber material is stiff, standard, and compliant, respectively.(b) EDPVR curves for (left) ventricles of Wistar rats (yellow), red-eared slider turtles (blue), masu salmon (light green), and cherry salmon (magenta).(c) EDPVR plots in which the previous curves (B) were normalized by their corresponding ventricular weights.The horizontal axis represents ventricular volume normalized by ventricular weight.